Problem: Solve for $x$ and $y$ using substitution. ${3x+2y = -3}$ ${x = -2y+11}$
Since $x$ has already been solved for, substitute $-2y+11$ for $x$ in the first equation. ${3}{(-2y+11)}{+ 2y = -3}$ Simplify and solve for $y$ $-6y+33 + 2y = -3$ $-4y+33 = -3$ $-4y+33{-33} = -3{-33}$ $-4y = -36$ $\dfrac{-4y}{{-4}} = \dfrac{-36}{{-4}}$ ${y = 9}$ Now that you know ${y = 9}$ , plug it back into $\thinspace {x = -2y+11}\thinspace$ to find $x$ ${x = -2}{(9)}{ + 11}$ $x = -18 + 11$ ${x = -7}$ You can also plug ${y = 9}$ into $\thinspace {3x+2y = -3}\thinspace$ and get the same answer for $x$ : ${3x + 2}{(9)}{= -3}$ ${x = -7}$